Substellar mass function and maximum baryonic mass in the halo of the Galaxy

We use recently observed luminosity functions of halo M-dwarfs and an accurate mass-luminosity relationship to derive the mass function of Pop II low-mass stars in the galactic spheroid. All these luminosity functions yield rising mass functions near the hydrogen-burning limit (with $\alpha\approx 2$). Connecting the microlensing and star count constraints, we show that the mass function in the dark halo steepens significantly ($\alpha \gtrsim 4$). The minimum mass is found to be $m_{\rm inf}\approx 0.02 M_\odot$, which corresponds to an average mass $\overline{m}\approx 0.03 M_\odot$, strongly suggesting that the dark objects responsible for the microlensing events are genuine brown dwarfs. We determine the expected spheroid and halo brown-dwarf density in the solar neighbourhood. The mass fraction under the form of substellar objects in the halo of the Galaxy is likely to represent only 5 to 15 % of the total dynamic mass